A multiscale model for traffic regulation via autonomous vehicles

Abstract

Autonomous vehicles (AVs) allow new ways of regulating the traffic flow on road networks. Most of available results in this direction are based on microscopic approaches, where ODEs describe the evolution of regular cars and AVs. In this paper, we propose a multiscale approach, based on recently developed models for moving bottlenecks. Our main result is the proof of existence of solutions for open-loop controls with bounded variation.

Model-based assessment of the impact of driver-assist vehicles using kinetic theory

“…[15,16,36,49], or propose a heuristic embedding of point particles, representing the driver-assist vehicles, in a continuous flow of standard vehicles, see e.g. [18,26]. It is worth mentioning that control problems in connection with kinetic equations are an active research line, which has been recently investigated in the context of selforganisation and games to reproduce competitive scenarios and to force the emergence of patterns, see [3][4][5].…”

A Macroscopic Traffic Flow Model Accounting for Bounded Acceleration

“…Since f is Lipschitz continuous, and since ρ N converges towards ρ in the L 1 norm, we can apply the dominated convergence theorem to conclude that ρ is a weak solution of (2.1a), (2.1c) (see also [15]).…”

“…for t n i,N defined in (3.5). Passing to the limit in (4.5), by Lemma 3 and the convergence of speed traces also in the presence of non-classical shocks [15,26], one gets (4.6) min At + v(ρ 0 (y…”

“…The idea of modeling the interaction of specific vehicles (like buses or trucks) with the surrounding traffic through strongly coupled PDE-ODE systems was introduced in [23] and then studied analytically in [11,15,19,27]. The interested reader is also referred to [4,7,12,32] for numerical treatments and extensions to second order models.…”

“…Following [11,15], solutions to (2.1) are intended in the weak sense specified below: Definition 1 (Entropy weak solution of the PDE-ODE model). Let T > 0 be a given finite time horizon.…”